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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 12 — Dec. 1, 1999
  • pp: 2845–2858

General method for deriving an XYZ tristimulus space exemplified by use of the Stiles–Burch1955 2° color matching data

Jan Henrik Wold and Arne Valberg  »View Author Affiliations


JOSA A, Vol. 16, Issue 12, pp. 2845-2858 (1999)
http://dx.doi.org/10.1364/JOSAA.16.002845


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Abstract

Using, as an example, the color matching functions of the StilesBurch1955 2° pilot group, we show how an XYZ representation of color space can be developed from a given set of color matching data. In doing this, we present a set of criteria that unequivocally defines the representation. The method outlined is general and can be applied to any set of color matching data, in particular those sets that are related to the physiological fundamentals.

© 1999 Optical Society of America

OCIS Codes
(330.0330) Vision, color, and visual optics : Vision, color, and visual optics
(330.1710) Vision, color, and visual optics : Color, measurement
(330.1720) Vision, color, and visual optics : Color vision
(330.1730) Vision, color, and visual optics : Colorimetry
(330.5310) Vision, color, and visual optics : Vision - photoreceptors

History
Original Manuscript: June 15, 1999
Manuscript Accepted: July 16, 1999
Published: December 1, 1999

Citation
Jan Henrik Wold and Arne Valberg, "General method for deriving an XYZ tristimulus space exemplified by use of the Stiles–Burch1955 2° color matching data," J. Opt. Soc. Am. A 16, 2845-2858 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-12-2845


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References

  1. F. Viénot, “Fundamental chromaticity diagram with physiologically significant axes,” in Proceedings of the Symposium ’96 on Colour Standards for Image Technology, Vienna, 1996 (Central Bureau of the CIE, Vienna, 1996), pp. 35–40.
  2. The CIE committee TC 1-36 distinguishes between the “fundamental response curves,” representing the fundamental spectral sensitivity functions of the three types of cones at the corneal level, and the “cone absorption curves,” which are derived by correcting the fundamentals by the absorption of the lens and ocular media and the macular pigment. Hence, if Tmedia(λ) denotes the spectral transmittance of the lens and ocular media and Tmacula(λ) denotes the spectral transmittance of the macular pigment, each cone absorption curve is given in terms of the corresponding fundamental response curve by the equation cone absorption curve=fundamental response curveTmedia(λ)Tmacula(λ).
  3. CIE, Proceedings of the 8th Session of the CIE, Cambridge, 1931 (Cambridge U. Press, Cambridge, UK, 1932), pp. 19–29.
  4. ISO/CIE, CIE Standard Colorimetric Observers, Publication ISO/CIE 10527 (Central Bureau of the CIE, Vienna, 1991).
  5. W. S. Stiles, J. M. Burch, “NPL colour-matching investigation: final report (1958),” Opt. Acta 6, 1–26 (1959). [CrossRef]
  6. R. Luther, “Aus dem Gebiet der Farbreizmetrik,” Z. Tech. Phys. 8, 540–558 (1927).
  7. D. I. A. MacLeod, R. M. Boynton, “Chromaticity diagram showing cone excitation by stimuli of equal luminance,” J. Opt. Soc. Am. 69, 1183–1186 (1979). [CrossRef] [PubMed]
  8. R. M. Boynton, “A system of photometry and colorimetry based on cone excitation,” Color Res. Appl. 11, 244–252 (1986). [CrossRef]
  9. CIE, , “Fundamental chromaticity diagram with physiological axes” (Central Bureau of the CIE, Vienna, 1998).
  10. W. S. Stiles, J. M. Burch, “Interim report to the Commission Internationale de l’Eclairage, Zürich, 1955, on the National Physical Laboratory’s investigation of colour-matching,” Opt. Acta 2, 168–181 (1955). [CrossRef]
  11. J. H. Wold, A. Valberg, “Cones for colorimetry,” in Proceedings of the 23rd Session of the CIE, New Delhi, 1995 (Central Bureau of the CIE, Vienna, 1995), Vol. 1, pp. 24–27.
  12. T. Smith, J. Guild, “The C.I.E. colorimetric standards and their use,” Trans. Opt. Soc. 33, 73–134 (1931–1932). [CrossRef]
  13. H. S. Fairman, M. H. Brill, H. Hemmendinger, “How the CIE 1931 color matching functions were derived from Wright-Guild data,” Color Res. Appl. 22, 11–23 (1997). [CrossRef]
  14. D. B. Judd, “Reduction of data on mixture of color stimuli,” Bur. Stand. J. Res. 4, 515–548 (1930). [CrossRef]
  15. D. L. MacAdam, Color Measurement: Theme and Variations (Springer-Verlag, Berlin, 1981).
  16. The CIE RGB representation refers to Wright primaries R, G, and B, representing monochromatic stimuli of wavelengths 700.0, 546.1, and 435.8 nm, respectively (see Refs. 3 and 17). The norms of R, G, and B are defined so as to ensure that the chromaticity coordinates of Illuminant E are rE=gE=bE=1/3.
  17. W. D. Wright, “A re-determination of the trichromatic coefficients of the spectral colours,” Trans. Opt. Soc. 30, 141–164 (1928–1929). [CrossRef]
  18. E. Schrödinger, “Über das Verhältnis der Vierfarben- zur Dreifarbentheorie,” Sitzungber. Kaiserl. Wien. Akad. Wiss. Math.-Naturwiss. Kl. 134, Abt. IIa, 471–490 (1925).
  19. CIE, Proceedings of the 6th Session of the CIE, Geneva, July 1924 (Cambridge U. Press, Cambridge, UK, 1926), pp. 67–70.
  20. Other constraints have also been considered. For instance, D. Brainard (topical editor, 1999, personal communication) has suggested minimizing the difference between CMF’s (Judd–Vos versus Stiles–Burch1955) rather than between the spectral loci of the chromaticity diagrams. This alternative seemed most attractive because of its simplicity. However, it turns out that such a minimization of differences of tristimulus values in three dimensions leads to severe and considerable distortions of the chromaticity diagram (see Refs. 21 and 22). Yet another alternative would be to let the tristimulus vector to which the fundamental S-response curve (S fundamental) refers serve as the Z primary. (See Section 8 for further details.)
  21. J. H. Wold, A. Valberg, “A comparison of two principles for deriving XYZ tristimulus spaces,” in The 15th Symposium of the International Colour Vision Society, Göttingen, July 1999, Abstract P40.
  22. J. H. Wold, A. Valberg, “The derivation of XYZ tristimulus spaces: a comparison of two alternative methods,” Color Res. Appl. (to be published).
  23. D. B. Judd, “CIE Technical Committee No. 7 “Colorimetry and artificial daylight,” Report of Secretariat United States Committee,” in Proceedings of the 12th Session of the CIE, Stockholm, 1951 (Bureau Central de la CIE, Paris, 1951), Vol. 1, Part 7, pp. 1–60.
  24. J. J. Vos, “Colorimetric and photometric properties of a 2° fundamental observer,” Color Res. Appl. 3, 125–128 (1978). [CrossRef]
  25. S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, M. M. Patterson, “Factors affecting luminance additivity at threshold among normal and color-blind subjects and elaborations of a trichromatic-opponent colors theory,” Vision Res. 8, 913–928 (1968). [CrossRef] [PubMed]
  26. V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975). [CrossRef] [PubMed]
  27. A. Eisner, D. I. A. MacLeod, “Blue-sensitive cones do not contribute to luminance,” J. Opt. Soc. Am. 70, 121–123 (1980). [CrossRef] [PubMed]
  28. W. Verdon, A. J. Adams, “Short-wavelength-sensitive cones do not contribute to mesopic luminosity,” J. Opt. Soc. Am. A 4, 91–95 (1987). [CrossRef] [PubMed]
  29. The contribution of the S cones to luminance has been somewhat contentious. Some authors claim that S cones do make a small contribution, whereas others maintain that they do not. However, given that the contribution, if any, is minor, it is convenient to assume that the S-cone contribution is zero. See, for instance, A. Stockman, L. T. Sharpe, “Cone spectral sensitivities and color matching,” in Color Vision: From Genes to Perception, K. R. Gegenfurtner, L. T. Sharpe, eds. (Cambridge U. Press, Cambridge, U.K., 1999).
  30. A. Stockman, D. I. A. MacLeod, N. E. Johnson, “Spectral sensitivities of the human cones,” J. Opt. Soc. Am. A 10, 2491–2521 (1993). [CrossRef]
  31. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).
  32. In the paper by Stockman et al.,30 the proposed values are 0.68237 and 0.35235. If we apply these values, the maximum of V⋅(λ) turns out to be 0.999777 (at 553 nm). To normalize V⋅(λ) to a maximum value of 1.000000, the coefficients are multiplied by the factor 1/0.999777.
  33. O. Estévez, “On the fundamental data-base of normal and dichromatic color vision,” Ph.D. dissertation (Amsterdam University, Krips Repro Meppel, Amsterdam, 1979).
  34. J. H. Wold, A. Valberg, “Mathematical description of a method for deriving an XYZ tristimulus space,” Department of Physics Report Series (University of Oslo, Oslo, 1999).
  35. CIE, CIE 1988 2° Spectral Luminous Efficiency Function for Photopic Vision, 1st ed., Publication CIE No. 86 (Central Bureau of the CIE, Vienna, 1990).
  36. H. G. Sperling, “An experimental investigation of the relationship between colour mixture and luminous efficiency,” in Visual Problems of Colour (Her Majesty’s Stationery Office, London, 1958), Vol. 1, pp. 249–247.
  37. J. H. Wold, “Colorimetric transformation equations allowing flexible normalization,” Die Farbe (to be published).
  38. A computer program (written in Mathematica) that determines the coefficient of the transformations that convert a given set of color matching data into a corresponding XYZ representation may be obtained from the authors on request.

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